1. Field of the Invention
The invention relates to a method for measuring the optical path difference of an imbalanced interferometer using a wavelength modulated laser. More specifically, the method includes the step of measuring the frequency of the optical fringes generated by modulating the wavelength of the laser.
The invention also relates to a system for carrying out the method.
2. Description of Prior Art
Optical interferometer measurement systems are known in the prior art as described in, for example, U.S. Pat. No. 4,767,210, which teaches an interferometer having a reference arm and a sensing arm of unequal lengths.
"Distance Sensing and Tunable Laser Characterization using an All Fiber-Optic Interferometer", SPIE, Vol. 746, Industrial Laser Interferometry 1987, pps. 37 et seq., Strzelecki et al, uses interferometeric methods and a tunable laser for measuring distances. "Close Loop FM Interferometric Remote Optical Fiber Sensor", PROC. SPIE Technical Symposium East 83, Vol. 412, Fiber Optic and Laser Sensors, pps. 256 et seq., Giles et al, teaches an approach wherein the path imbalance of an interferometer is measured using a frequency modulated laser.
One of the major problems in developing optical interferometric sensor systems has been the lack of effective methods to determine the optical path difference. The output intensity of an interferometric sensor, e.g. a Mach-Zehnder interferometer, can be expressed as: ##EQU1## where I.sub.out and I.sub.in denote, respectively, the output and input intensity of the interferometer, .lambda. is the wavelength of the light source, and .DELTA. is the optical path difference. When a single mode laser is used as a light source of the sensor, the difficulty in measuring .DELTA. arises from the periodicity of the cosine function. In a rather simplified example, if cos ##EQU2## is determined as being equal to 0, then ##EQU3## is equal to ##EQU4## where n is equal to any odd integer. Given that .lambda. is fixed, the value of .DELTA. is directly related to the value of n. However, the system cannot measure the value of n, it can merely determine that cos is equal to 0.
Accordingly, a typical sensor must be able to resolve the changes in .DELTA. from a fraction of a .lambda. to possibly hundreds of .lambda.s.
One of the methods for measuring .DELTA. is to modulate the wavelength of the laser, i.e., to frequency modulate the laser. See, for example, "Distance Sensing and Tunable Laser Characterization Using an All Fiber-optic Interferometer", SPIE Vol. 746, Industrial Laser Interferometry, p 37, 1987, Strzelecki et al. However, this method is limited for sensor applications, due to the fact that when a laser diode is used, only a very . small wavelength deviation; typically less than a few angstroms, can be achieved before mode hoppings occur. See "Close Loop FM Interferometric Remote Optical Fiber Sensor", Proc. SPIE Technical Symposium East 83, Vol. 412, Fiber Optic and Laser Sensors, p 256, 1983, Uttam et al.
Using an imbalanced interferometer rather than the traditional balance interferometer has the advantage of increasing the sensitivity of the sensor to wavelength changes. Consider the phase of the output intensity from a sensor: ##EQU5##
The relative change corresponding to the frequency modulation is given by ##EQU6## where ##EQU7##
For a balanced interferometer, where K is very close to 0, a large range of wavelength changes is required to achieve a desired phase change. By introducing an imbalanced interferometer with a large K, d.phi. can be significantly increased. For example, when ##EQU8## an imbalanced interferometer with K approximately equal to 4000 will go through two fringes (d.phi.=2.times.2 .pi.).